Magnetic Islands and Confinement of Charged Particlesin Toroidal Magnetic Systems

Results of the study of charged particle trajectories in a toroidal magnetic configuration like tokamak with “magnetic islands” are presented. Particle trajectories are calculated using the three-dimensional numerical code based on numerical integration of exact equations of motion. Magnetic configuration is described analytically with use of an universal approach in terms of Hamiltonian function. This approach generalizes the traditional streaming presentation of magnetic field and guaranties the solenoidality condition being satisfied exactly. To describe magnetic configuration with islands, iterative procedure is used; the initial (basic) magnetic configuration is chosen to have nested magnetic surfaces. Small helical perturbation splits the rational surface resonant with the perturbation helicity. In the vicinity of such surface the chain of magnetic islands is formed. Our study of the motion of charged particles showed that the existence of the magnetic island has no qualitative impact on the Poincare cross-section of the trapped particle trajectory for having a standard “banana” form, typical for basic tokamak configuration. As for passing particle, which moves predominantly along the magnetic field line, its trace of the trajectory has an island structure in the poloidal cross-section. It is shown that both trapped and passing particles in their motion can cross the separatrix between magnetic island and nested magnetic surfaces; the crossing can happen in any point of separatrix. Thus, it is shown that the magnetic island has no “barrier” properties and isn’t capable to provide the improved confinement of charged particles.

plasma, toroidal configurations, tokamak, magnetic surface, magnetic island, Hamiltonian description